The present invention relates to tensile testing of membrane materials, and more particularly to an apparatus and method for biaxial tensile testing of membrane materials.
Traditionally, the tensile properties of fabrics are evaluated in uniaxial testing in which force-deformation response of a fabric is measured along one of the major axes (machine or cross). Results of uniaxial tests produce indices of relative tensile behavior but are inadequate for many applications. However, in actual use, the textile fabrics rarely experience true uniaxial forces. In most instances, the forces are imposed simultaneously in more than one direction resulting in responses that are quite different from that under uniaxial force. Since most fabrics or orthotropic membranes possess two principal directions and the forces or deformations in most cases can be resolved into two orthogonal components, it is important to understand their behavior under two dimensional force or deformation. Application of forces or extensions simultaneously along two orthogonal axes is referred to as xe2x80x9cbiaxialxe2x80x9d.
Often, the objective of tensile testing of fabrics is to characterize their nature of failure in terms of breaking elongation and strength. However, for many applications it may be more important to find out the relationships between applied stresses (or strains) and resultant strains (or stresses), e.g.,
"sgr"x=f1(xcex5x,xcex3y,xcex3xy),"sgr"y=f2(xcex5x,xcex5y,xcex3xy),"sgr"xy=f3(xcex5x,xcex5y,xcex3xy)
where "sgr"x and "sgr"y are stresses in machine and cross directions, respectively, and "sgr"xy is the shear stress. Similarly, xcex5x and xcex5y are strains in machine and cross directions, and xcex3xy is the shear strain. These constitutive relationships between stress-strain parameters are well known for linear orthotropic materials. However, the stress-strain relationships of textile fabrics are far more complex and non-linear.
The need to measure the constitutive laws of fabric behavior, in addition to studying their nature of failure, has received considerable attention in the literature. A number of studies have been reported in the area of theoretical modeling of fabric deformation under uniaxial as well as biaxial tensile forces. Other researchers have reported various experimental methods of evaluating fabric behavior under biaxial tensile forces.
Multi-directional test devices have been described by Ariano (xe2x80x9cRubber Stretched by Forces in Two Directions Perpendicular to one Anotherxe2x80x9d, Rubber Chemistry and Technology, 13, 92-102 (1942)) as early as 1942. He developed a static two-dimensional tester for rubber films. Anderson (xe2x80x9cA Method for Obtaining Stress-Strain Relations in Non-Isotropic Flexible Sheet Material Under Two-Dimensional Stressxe2x80x9d, Journal of Scientific Instruments, 24, 25 (1947)) and Boonstra (xe2x80x9cStress-Strain Properties of Natural Rubber under Biaxial Strainxe2x80x9d, Journal of Applied Physics, 21, 1098-1104 (1950)) used a pressure cylinder apparatus suitable for impermeable sheet materials. Treloar (xe2x80x9cThe Swelling of Cross-Linked Amorphous Polymer under Strainxe2x80x9d, Transactions of Faraday Society, 46, 783-789 (1950)) developed an apparatus for imposing four-directional planar strains in rubber, but without any provision for measuring forces. The two-dimensional force-extension tester reported by Reichard, Woo, and Montgomery (xe2x80x9cA Two Dimensional Load-Extension Tester for Woven Fabricsxe2x80x9d, Textile Research Journal, 23, 424-4248 (1953)) and later used by Woo, Dillon, and Dusenbury (xe2x80x9cThe Reaction of Formaldehyde with Cellulosic Fibers, Part II: Mechanical Behaviorxe2x80x9d, Textile Research Journal, 26, 761-783 (1956)) is a modified uniaxial tensile tester that was designed to extend a fabric along two perpendicular directions. However, the instrument could measure the force developed in one direction only under moderate levels of strain. Checkland. Bull, and Bakker (xe2x80x9cA Two-Dimensional Load-Extension Tester for Fabrics and Filmxe2x80x9d, Textile Research Journal, 28, 399-403 (1958)) reported a two-dimensional force extension tester in which a four-jaw, self-centering lathe chuck was used as the straining device. The sample size was quite small, as was the strain level.
All these devices were equipped with solid clamps that did not allow any deformation along the clamps, a critical requirement, for large or finite deformation. Additionally, none of the above investigators either defined or examined the role of control variables in interpreting their experimental results. Of the multi-directional testers already reviewed, only two were specifically designed for and readily applicable to the laboratory testing of fabrics. In both cases, the clamps were moved at constant rates to apply strains in the sample. However, as Klein (xe2x80x9cStress-Strain Response of Fabrics underTwo-Dimensional Loading, Part I: The FRL Biaxial Testerxe2x80x9d, Textile Research Joumal, 29, 816-821 (1959)) pointed out, in both cases neither the forces nor the extensions are controlled in the central region of the test specimen. Thus, while general trends in biaxial behavior can be determined from these machines, considerable generality is lost and quantitative comparison of different materials is rather impossible.
Klein described a biaxial tester with solid clamps and proposed a set of design criteria for a biaxial tester based on sound theoretical analysis. He pointed out that in a biaxial testing system, either both forces or both extensions must be specified or controlled while the other should be measured. Klein chose forces as independent variables because of his particular requirements. He then concluded that a biaxial test could be considered completely controlled and reproducible by the control of a single factor, i.e., the ratio of forces or extension in the two directions. Klein designed his instrument to measure force-extension behavior of a cruciform sample (2 in.xc3x972 in.) under different levels of force-ratio.
Freeston et al. (xe2x80x9cMechanics of Elastic Performance of Textile Materials, Part 18. Stress-Strain Response of Fabrics under Two Dimensional Loadingxe2x80x9d, Textile Research Journal, 37, 948-975 (1967)) in 1967 reported a biaxial tester developed by the Air Force Materials Laboratory. The load-frame of the test system described by Freeston et al. was similar to Klein. However, the clamping system of this instrument was designed to rotate freely about an axis perpendicular to the plane of the test specimen to permit shear deformations.
An important factor to be considered in biaxial testing of fabrics or other similar membranes is the distribution of stress and strain in the test specimen. Perfect homogeneity of strain in a test device is almost always unattainable. However, test instruments must be designed to minimize the variations of stress and strain. None of the prior art instruments described thus far allow for homogeneous distribution of stress and strain. In testing a flat specimen of a membrane/fabric, it is necessary to allow the specimen to undergo tensile strain in the direction along each clamp. In the vicinity of the solid clamps, these strains are not allowed to develop. Consequently, these xe2x80x9cboundary effectsxe2x80x9d become particularly severe in cases of small samples.
A number of testers reported in the literature have provided for deformation along each clamp. Two of these, Rivlin et al. (xe2x80x9cLarge Elastic Deformations of Isotropic Materials, VII: Experiments on the Deformation of Rubberxe2x80x9d, Philosophical Transactions of the Royal Society, 243, 251-288 (1951)) and McRory et al. (xe2x80x9cExperimental Investigation of the Biaxial Load-Extension Properties of Plain, Weft-Knitted Fabricsxe2x80x9d, Textile Research Journal, 47, 233-239 (1977)) applied stresses with what was essentially point contact, while Sakaguchi et al. (Journal of the Society of Materials Science, Japan, 17, 365 (1968)) and Kawabata et al. (xe2x80x9cThe Finite-Deformation Theory of Plain-Weave Fabrics, Part 1: The Biaxial-Deformation Theoryxe2x80x9d, Joumal of The Textile Institute, 64, 21-46 (1973) and xe2x80x9cNonlinear Theory of the Biaxial Deformation of a Triaxial-Weave Fabricxe2x80x9d, Joumal of The Textile Institute) used segmented clamps of finite area. Several testers used specimens with tabs protruding from the edges in order to help induce a homogeneous stress distribution in the center of the specimen. However, the tester of McRory et al. used a specimen with straight edges, and relied upon closer spacing of the grip points (0.25 cm) to distribute the stresses. While the segmented clamping system improved the homogeneity of the strain distribution, edge effects were still present in the stress and strain measurement system. The edge effects can be reduced to some extent by measuring the stress and strain only over the central part of the specimen. However, selective measurement of stress is difficult. Kawabata et al. used the instrument mentioned earlier, but with a modification such that stress was measured only over the center sections of the sides of the specimen. This was achieved by attaching the corner clamp-grips to members other than the xe2x80x9cload-detection-barsxe2x80x9d, to which central clamps and force transducers were attached. Riviin used another approach of individual adjustment of clamps to address this problem. It is worth observing that Sakaguchi et al. and Kawabata et al. used ratio of strain in the two directions as the control parameter of their testing as opposed to force-ratio.
While these segmented clamping systems improved the homogeneity of the strain distribution, frictional forces within the clamp segments and edge effects were still present in the system. In segmented clamps, an extension in the X-direction is accommodated by tabs in the Y-direction by pulling on the Y-direction clamp-segments laterally at an angle other than zero. In other words, the force necessary to move the Y-direction clamp-segments is provided by the X-direction clamps and transmitted through the tabs in Y-direction. Even a small frictional resistance to this movement will cause inhomogeneity in the strain field of the test sample. More importantly, it develops stress concentrations at the joining point of the adjacent Y-direction tabs, which promote tear into the test area. The same can be said about an extensional displacement of the Y-direction clamps and corresponding adjustment by the X-direction clamp-segments.
Thus, the search continues in biaxial testing for a suitable clamp system that will allow for unhindered strain to occur in a test sample, in particular, near the edges while extending the capacity of load-frames to useful levels.
In accordance with the present invention, applicant provides an apparatus for biaxial load deformation testing of textile and other membrane materials that provides for unhindered strain to occur in the sample near the edges so as to obviate significant xe2x80x9cboundary effectsxe2x80x9d during deformation testing. The apparatus comprises a first pair of spaced-apart segmented clamping systems for detachably engaging a membrane test material along opposing sides extending in a first (X) direction wherein the clamping systems each comprise a plurality of clamps interconnected by a pantograph so as to be slidably extendable and slidably contractible with respect to each other. A second pair of spaced-apart segmented clamping systems is provided for detachably engaging a membrane test material along opposing sides extending in a second (Y) direction orthogonal to the first direction wherein the clamping systems each comprise a plurality of clamps interconnected by a pantograph so as to be slidably extendable and slidably contractible with respect to each other. A first drive system is used for moving the first pair of segmented clamping systems apart from each other so as to impart a predetermined strain in the second (Y) direction, and a second drive system is provided for moving the second pair of segmented clamping systems apart each from the other so as to impart a predetermined strain in the first (X) direction. A first linkage system operatively interconnecting the first and second pair of segmented clamping systems is provided so as to slidably extend the second pair of segmented clamping systems in the second (Y) direction proportional to strain imparted to a membrane test material in the second (Y) direction when the first pair of segmented clamping systems is caused to move apart in the second (Y) direction by the first drive system. Further, a second linkage system operatively interconnecting the first and second pair of segmented clamping systems is provided so as to slidably extend the first pair of segmented clamping systems in the first (X) direction proportional to strain imparted to a test membrane in the first (X) direction when the second pair of clamping systems is caused to move apart in the first (X) direction by the second drive system.
Also in accordance with the present invention, applicant provides a method for biaxial load deformation testing of textile and other membrane materials so as to provide for unhindered strain to occur in the sample near the edges during deformation. The method includes providing a first pair of spaced-apart segmented clamping systems for detachably engaging a membrane test material along opposing sides extending in a first (X) direction wherein the clamping systems each comprise a plurality of clamps pantographically interconnected so as to be slidably extendable and slidably contractible with respect to each other. The method further includes providing a second pair of spaced-apart segmented clamping systems for detachably engaging a membrane test material along opposing sides extending in a second (Y) direction orthogonal to the first direction wherein the clamping systems each comprises a plurality of clamps pantographically interconnected so as to be slidably extendable and slidably contractible with respect to each other. The method further comprises driving the first pair of segmented clamping systems apart from each other to impart a predetermined stress and/or strain in the second (Y) direction and thereby causing the operatively connected second pair of segmented clamping systems to slidably extend in the second (Y) direction proportional to the strain imparted to a membrane test material in the second (Y) direction. Finally, the method provides for driving the second pair of segmented clamping systems apart from each other to impart a predetermined stress and/or strain in the first (X) direction and thereby causing the operatively connected first pair of segmented clamping systems to slidably extend in the first (X) direction proportional to the strain imparted to a membrane test material in the first (X) direction.
It is therefore an object of the present invention to provide an apparatus and method for biaxial load deformation testing of textile and other membrane materials that allows for unhindered strain to occur near the test sample edges so as to obviate boundary effects during testing.
It is another object of the present invention to provide an apparatus and method for biaxial load deformation testing of textile and other membrane materials that utilizes segmented and self-adjusting clamping systems to engage the four edges of a test sample so as to allow for finite biaxial deformation without suffering any significant undesirable boundary effects during testing.
It is still another object of the present invention to provide an apparatus and method for biaxial load deformation testing of textile and other membrane materials which serves to minimize the stress concentrations and strain inhomogeneities during biaxial load deformation testing of textile and other membrane materials.
It is still another object of the present invention to provide an apparatus and method for biaxial load deformation testing of textile and other membrane materials that uses an improved segmented clamping system for gripping deformable membrane materials during biaxial testing thereof.
Some of the objects of the invention having been stated, other objects will become evident as the description proceeds, when taken in connection with the accompanying drawings described hereinbelow.